Context. More than two thousand exoplanets have been discovered to date. Of these, only a small fraction have been detected around solar twins, which are key stars because we can obtain accurate elemental abundances especially for them, which is crucial for studying the planet-star chemical connection with the highest precision. Aims. We aim to use solar twins to characterise the relationship between planet architecture and stellar chemical composition. Methods. We obtained high-precision (1 m s-1) radial velocities with the HARPS spectrograph on the ESO 3.6 m telescope at La Silla Observatory and determined precise stellar elemental abundances (~0.01 dex) using spectra obtained with the MIKE spectrograph on the Magellan 6.5 m telescope. Results. Our data indicate the presence of a planet with a minimum mass of 26 ± 4 Earth masses around the solar twin HIP 68468. The planet is more massive than Neptune (17 Earth masses), but unlike the distant Neptune in our solar system (30 AU), HIP 68468c is close-in, with a semi-major axis of 0.66 AU, similar to that of Venus. The data also suggest the presence of a super-Earth with a minimum mass of 2.9 ± 0.8 Earth masses at 0.03 AU; if the planet is confirmed, it will be the fifth least massive radial velocity planet candidate discovery to date and the first super-Earth around a solar twin. Both isochrones (5.9 ± 0.4 Gyr) and the abundance ratio [Y/Mg] (6.4 ± 0.8 Gyr) indicate an age of about 6 billion years. The star is enhanced in refractory elements when compared to the Sun, and the refractory enrichment is even stronger after corrections for Galactic chemical evolution. We determined a nonlocal thermodynamic equilibrium Li abundance of 1.52 ± 0.03 dex, which is four times higher than what would be expected for the age of HIP 68468. The older age is also supported by the low log () (-5.05) and low jitter (<1 m s-1). Engulfment of a rocky planet of 6 Earth masses can explain the enhancement in both lithium and the refractory elements. Conclusions. The super-Neptune planet candidate is too massive for in situ formation, and therefore its current location is most likely the result of planet migration that could also have driven other planets towards its host star, enhancing thus the abundance of lithium and refractory elements in HIP 68468. The intriguing evidence of planet accretion warrants further observations to verify the existence of the planets that are indicated by our data and to better constrain the nature of the planetary system around this unique star.
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